No door ever closed but another one opened

Cha do dhùin doras nach do dh'fhosgail doras

Here are two more Gaelic idioms which feature nach

Am fear air nach tàinig, thig 
He who has not yet tasted misfortune, will  [lit. The man on whom it hasn't come, it will come] 
Cha do smaoinich nach do rinn 
Thoughts are the seeds of deeds   [lit. Not thought, not done